Megascale centripetal forces

This question may sound ignorant. When it comes to physics, I guess you could say I'm physically challenged. Still, I would appreciate any and all help given.

Assume a future, highly advanced human civilization built a spaceship at the edge of the galaxy. The ship slowly started accelerating, and did not cease until it reached 99.99 percent the speed of light. It then orbited around the galaxy, thus making a complete trip around roughly once every 300,000 years. At this distance, and at this speed, would they be able to notice, and/or survive the centripetal forces?

This question may sound ignorant. When it comes to physics, I guess you could say I'm physically challenged. Still, I would appreciate any and all help given.

Some people who are not completely familiar with physics ask questions and learn. Some others who are not completely familiar will attempt to "disprove" physics. I'm always happy to see more of the former :)

Assume a future, highly advanced human civilization built a spaceship at the edge of the galaxy.

OK... for the sake of clarity, let's say the edge of the galaxy is about 47,750 lightyears from the center so later on we can calculate the circumference of the galaxy using 2 * pi * r.

The ship slowly started accelerating, and did not cease until it reached 99.99 percent the speed of light.

At this point, the question becomes a little vague for applying Special Relativity. You say the speed reaches 99.99% c, but to whom is this speed with respect to? In other words, where is the person/equipment located that is measuring this speed?

It then orbited around the galaxy, thus making a complete trip around roughly once every 300,000 years.

It takes 300,000 years for whom? The inhabitants of the ship?

At this distance, and at this speed, would they be able to notice, and/or survive the centripetal forces?

Well, I'm going to wait for your response to my questions before plugging and chugging. I, however, have a strong suspicion that all the numbers you mentioned are with respect to someone on Earth or some other planet in the galaxy (the numbers you bring up seem to make more sense that way).

p.s. Remember, it's called relativity because it's all relative with respect to a frame of reference.

I did mean relative to someone on earth, but come to think of it, perhaps that wasn't the best reference point. Earth also moves (around the sun, and with the rotation of the galaxy), which might add more complicated calculations for ITS speed as well as the spaceship's. Since I'm not all that well versed in mathematics, either, I'd like to keep this as simple as possible. So now that I think about it, I should instead use as a reference point some people/persons who is/are, more or less, at some point that is completely still in space.

Not earth. Just a deep space station that is as completely still as possible.